Problem: Complete the square to solve for $x$. $x^{2}-18x+77 = 0$
Explanation: Begin by moving the constant term to the right side of the equation. $x^2 - 18x = -77$ We complete the square by taking half of the coefficient of our $x$ term, squaring it, and adding it to both sides of the equation. Since the coefficient of our $x$ term is $-18$ , half of it would be $-9$ , and squaring it gives us ${81}$ $x^2 - 18x { + 81} = -77 { + 81}$ We can now rewrite the left side of the equation as a squared term. $( x - 9 )^2 = 4$ Take the square root of both sides. $x - 9 = \pm2$ Isolate $x$ to find the solution(s). $x = 9\pm2$ So the solutions are: $x = 11 \text{ or } x = 7$ We already found the completed square: $( x - 9 )^2 = 4$